"use strict"; const {Fragment: _Fragment, jsx: _jsx, jsxs: _jsxs} = arguments[0]; const {useMDXComponents: _provideComponents} = arguments[0]; function _createMdxContent(props) { const _components = { a: "a", code: "code", figure: "figure", h2: "h2", img: "img", li: "li", p: "p", pre: "pre", span: "span", ul: "ul", ..._provideComponents(), ...props.components }; return _jsxs(_Fragment, { children: [_jsx(_components.p, { children: _jsx(_components.a, { href: "https://www.acmicpc.net/problem/12865", children: "문제 링크" }) }), "\n", _jsx(_components.h2, { children: "문제" }), "\n", _jsx(_components.p, { children: "이 문제는 아주 평범한 배낭에 관한 문제이다." }), "\n", _jsx(_components.p, { children: "한 달 후면 국가의 부름을 받게 되는 준서는 여행을 가려고 한다. 세상과의 단절을 슬퍼하며 최대한 즐기기 위한 여행이기 때문에, 가지고 다닐 배낭 또한 최대한 가치 있게 싸려고 한다." }), "\n", _jsx(_components.p, { children: "준서가 여행에 필요하다고 생각하는 N개의 물건이 있다. 각 물건은 무게 W와 가치 V를 가지는데, 해당 물건을 배낭에 넣어서 가면 준서가 V만큼 즐길 수 있다. 아직 행군을 해본 적이 없는 준서는 최대 K만큼의 무게만을 넣을 수 있는 배낭만 들고 다닐 수 있다. 준서가 최대한 즐거운 여행을 하기 위해 배낭에 넣을 수 있는 물건들의 가치의 최댓값을 알려주자." }), "\n", _jsx(_components.h2, { children: "입력" }), "\n", _jsx(_components.p, { children: "첫 줄에 물품의 수 N(1 ≤ N ≤ 100)과 준서가 버틸 수 있는 무게 K(1 ≤ K ≤ 100,000)가 주어진다. 두 번째 줄부터 N개의 줄에 거쳐 각 물건의 무게 W(1 ≤ W ≤ 100,000)와 해당 물건의 가치 V(0 ≤ V ≤ 1,000)가 주어진다." }), "\n", _jsx(_components.p, { children: "입력으로 주어지는 모든 수는 정수이다." }), "\n", _jsx(_components.h2, { children: "출력" }), "\n", _jsx(_components.p, { children: "한 줄에 배낭에 넣을 수 있는 물건들의 가치합의 최댓값을 출력한다." }), "\n", _jsx(_components.h2, { children: "풀이" }), "\n", _jsx(_components.p, { children: "각 물건은 한 번만 선택할 수 있고, 배낭의 허용 무게 안에서 가치 합을 최대화해야 하므로 전형적인 0/1 배낭 문제다. 상태를 dp[i][w]처럼 두고 i번째 물건까지 고려했을 때 무게 w에서 얻을 수 있는 최대 가치를 저장하면 된다." }), "\n", _jsx(_components.p, { children: "코드에서도 현재 물건을 넣지 않는 경우 dp[i - 1][w]와, 넣을 수 있다면 dp[i - 1][w - weight[i]] + value[i]를 비교해 더 큰 값을 선택한다. 이렇게 하면 각 물건을 사용할지 말지가 자연스럽게 반영된다." }), "\n", _jsx(_components.p, { children: "중요한 점은 같은 물건을 여러 번 쓰지 않는다는 것이다. 현재 줄의 값을 같은 줄 갱신에 재사용하지 않고, 항상 이전 물건까지의 결과에서 넘어오도록 만들면 0/1 조건이 정확히 지켜진다." }), "\n", _jsx(_components.h2, { children: "코드" }), "\n", _jsx(_components.figure, { "data-rehype-pretty-code-figure": "", children: _jsx(_components.pre, { style: { backgroundColor: "#2e3440ff", color: "#d8dee9ff" }, tabIndex: "0", "data-language": "cpp", "data-theme": "nord", children: _jsxs(_components.code, { "data-language": "cpp", "data-theme": "nord", style: { display: "grid" }, children: [_jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#5E81AC", fontWeight: "bold" }, children: "#" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "include" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " <" }), _jsx(_components.span, { style: { color: "#A3BE8C" }, children: "iostream" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ">" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#5E81AC", fontWeight: "bold" }, children: "#" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "include" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " <" }), _jsx(_components.span, { style: { color: "#A3BE8C" }, children: "algorithm" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ">" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "using" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " namespace" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " std" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "int" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " weight" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: "101" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]," }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " value" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: "101" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "int" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " dp" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: "101" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, 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}, children: "," }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " k" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "," }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " w" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "," }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " v" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\tcin " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ">>" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " n " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ">>" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " k" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\tfor" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " (" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "int" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " i " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "=" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 1" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " i " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "<=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " n" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " i" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "++" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " " })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "\t\tcin " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ">>" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " weight" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "i" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " >>" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " value" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "i" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#616E88" }, children: "\t//i: 배낭안에 담을 물건의 갯수 또는 i번째 물건, j: 물건의 총 무게, 값: 가치" }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\tfor" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " (" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "int" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " i " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "=" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 1" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " i " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "<=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " n" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " i" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "++" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " {" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\tfor" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " (" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "int" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " j " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "=" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 1" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " j " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "<=" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " k" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " j" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "++" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " {" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#616E88" }, children: "\t\t\t//현재 물건의 무게(weight[i])가 j보다 크다면, 물건을 담을 수 없는 상태" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#616E88" }, children: "\t\t\t//이전 배낭의 상태(물건의 갯수가 i - 1일 때)의 가치를 가져옴" }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\tif" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " (" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "j " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "<" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " weight" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "i" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "])" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " " })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9" }, children: "\t\t\t\tdp" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "i" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "][" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "j" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " =" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " dp" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "i " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "-" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 1" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "][" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "j" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#616E88" }, children: "\t\t\t//현재 물건의 무게가 같거나 작다면, 물건을 담을 수 있는 상태" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#616E88" }, children: "\t\t\t//이전 배낭의 상태와 i번째 물건을 담은 상태의 값 중 가치가 큰 값을 선택" }) }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#81A1C1" }, children: "\t\t\telse" }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9" }, children: "\t\t\t\tdp" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "i" }), _jsx(_components.span, { style: { 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_jsx(_components.span, { style: { color: "#D8DEE9" }, children: " dp" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "i " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "-" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 1" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "][" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "j " }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "-" }), _jsx(_components.span, { style: { color: "#D8DEE9" }, children: " weight" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "[" }), _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: "i" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "]]" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: " +" }), _jsx(_components.span, { style: { color: 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_jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: "int" }), _jsx(_components.span, { style: { color: "#88C0D0" }, children: " main" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "()" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: " {" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " " }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " ios_base" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "::" }), _jsx(_components.span, { style: { color: "#88C0D0" }, children: "sync_with_stdio" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "(" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "false" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9" }, children: "\tcin" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "." }), _jsx(_components.span, { style: { color: "#88C0D0" }, children: "tie" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "(" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "NULL" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#D8DEE9" }, children: "\tcout" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "." }), _jsx(_components.span, { style: { color: "#88C0D0" }, children: "tie" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "(" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: "NULL" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: ")" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#D8DEE9FF" }, children: " " }) }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#88C0D0" }, children: "\tsolve" }), _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "()" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: " " }), "\n", _jsxs(_components.span, { "data-line": "", children: [_jsx(_components.span, { style: { color: "#81A1C1" }, children: " return" }), _jsx(_components.span, { style: { color: "#B48EAD" }, children: " 0" }), _jsx(_components.span, { style: { color: "#81A1C1" }, children: ";" })] }), "\n", _jsx(_components.span, { "data-line": "", children: _jsx(_components.span, { style: { color: "#ECEFF4" }, children: "}" }) })] }) }) }), "\n", _jsx(_components.h2, { children: "복잡도" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["시간 복잡도: ", _jsx(_components.code, { children: "O(NK)" })] }), "\n", _jsxs(_components.li, { children: ["공간 복잡도: ", _jsx(_components.code, { children: "O(NK)" })] }), "\n"] }), "\n", _jsx(_components.h2, { children: "마무리" }), "\n", _jsx(_components.p, { children: "배낭 문제는 결국 물건을 넣을지 말지를 상태 전이로 바꾸는 문제다. 이전 물건까지의 결과에서만 넘어오도록 보면 0/1 조건도 깔끔하게 지킬 수 있다." }), "\n", _jsx(_components.p, { children: _jsx(_components.img, { src: "/generated/posts/algorithm/boj-12865/assets/1.png", alt: "" }) })] }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = { ..._provideComponents(), ...props.components }; return MDXLayout ? _jsx(MDXLayout, { ...props, children: _jsx(_createMdxContent, { ...props }) }) : _createMdxContent(props); } return { default: MDXContent };

BOJ 12865 - 평범한 배낭